A posteriori estimates for the stochastic total variation flow
Numerical Analysis
2022-11-09 v2 Numerical Analysis
Abstract
We derive a posteriori error estimates for a fully discrete time-implicit finite element approximation of the stochastic total variaton flow (STVF) with additive space time noise. The estimates are first derived for an implementable fully discrete approximation of a regularized stochastic total variation flow. We then show that the derived a posteriori estimates remain valid for the unregularized flow up to a perturbation term that can be controlled by the regularization parameter. Based on the derived a posteriori estimates we propose a pathwise algorithm for the adaptive space-time refinement and perform numerical simulation for the regularized STVF to demonstrate the behavior of the proposed algorithm.
Cite
@article{arxiv.2110.08002,
title = {A posteriori estimates for the stochastic total variation flow},
author = {Ľubomír Baňas and André Wilke},
journal= {arXiv preprint arXiv:2110.08002},
year = {2022}
}